Calculator
Formula Used
The nominal cutoff frequency is:
fc = 1 / (2πRC)
The time constant is:
τ = RC
The capacitive reactance is:
Xc = 1 / (2πfC)
The capacitor impedance is:
Zc = -j / (2πfC)
For an ideal low pass RC series filter:
H = Zc / (R + Zc)
For an ideal high pass RC series filter:
H = R / (R + Zc)
When a load is entered, the output part is paralleled with the load. The calculator then uses the complex voltage divider.
Gain dB = 20 log10(|H|)
Vout = Vin × |H|
How to Use This Calculator
- Select low pass or high pass output.
- Enter the resistor value and its unit.
- Enter the capacitor value and its unit.
- Enter the test frequency and input voltage.
- Add load resistance when the next stage affects output.
- Press the calculate button to view results.
- Use CSV or PDF buttons for downloadable reports.
Example Data Table
| Case | Filter | R | C | Frequency | Vin | Nominal fc | Expected Gain |
|---|---|---|---|---|---|---|---|
| Audio tone check | Low pass | 10 k ohm | 0.01 microfarad | 100 Hz | 5 V | 1591.55 Hz | 0.998 V/V |
| Cutoff test | Low pass | 10 k ohm | 0.01 microfarad | 1591.55 Hz | 5 V | 1591.55 Hz | 0.707 V/V |
| High pass check | High pass | 10 k ohm | 0.01 microfarad | 10000 Hz | 5 V | 1591.55 Hz | 0.988 V/V |
Understanding RC Series Filters
An RC series filter uses one resistor and one capacitor. The parts are placed in one signal path. The output is taken across one part. That choice creates either a low pass or high pass response. A low pass output is taken across the capacitor. It passes slow signals with small loss. It reduces fast signals as frequency rises. A high pass output is taken across the resistor. It blocks slow changes and passes faster signals.
Important Results
The cutoff frequency is the main design point. At this frequency, ideal output magnitude is about 70.7 percent. The gain is therefore minus 3.01 dB. The time constant shows charging speed. It equals resistance multiplied by capacitance. A larger resistor or capacitor lowers cutoff frequency. A smaller value raises it. Phase also changes with frequency. This shift matters in audio, sensors, timing, and control circuits.
Practical Design Notes
Real circuits are not perfectly ideal. Source resistance, component tolerance, and load resistance can move the response. This calculator includes an optional load value. It models the load in parallel with the output part. That gives a more realistic output estimate. It also reports impedance, current, reactance, and power. These values help when checking source limits. They also help with capacitor voltage ratings and resistor heating.
Using the Calculator Effectively
Start with the wanted cutoff frequency. Choose a capacitor value that is easy to buy. Then calculate the needed resistance. You can also test an existing circuit. Enter measured component values for better accuracy. Next, set the test frequency. Compare it with the cutoff value. Frequencies far below cutoff act differently from frequencies far above it. Review gain, output voltage, and phase together. Do not use gain alone. A circuit may have acceptable amplitude but poor timing. Export the results for lab notes. Use the example table to compare typical cases.
Accuracy And Safety
Use standard component ratings for final builds. Capacitors should handle the largest signal voltage. Resistors should handle expected heat. For high frequency work, lead length and board layout matter. Keep connections short when possible. For audio work, consider the next circuit stage. Its input resistance may act as a load and reduce accuracy during real testing.
FAQs
What is an RC series filter?
It is a filter made with one resistor and one capacitor in series. The output location decides whether it works as a low pass or high pass filter.
What is cutoff frequency?
Cutoff frequency is the point where ideal output falls to 70.7 percent of input. It is also called the minus 3 dB point.
Which output gives a low pass filter?
Take the output across the capacitor. Low frequencies pass with less loss, while higher frequencies are reduced.
Which output gives a high pass filter?
Take the output across the resistor. Low frequencies are reduced, while higher frequencies pass more easily.
Why is phase angle important?
Phase angle shows timing shift between input and output. It matters in audio, feedback loops, sensors, and timing circuits.
Does load resistance change the result?
Yes. A load can reduce output voltage and shift the response. This calculator can include load resistance for a better estimate.
Can I export my calculation?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a compact report.
Is this calculator suitable for real circuits?
It is useful for planning and checking. Real parts have tolerance, parasitic effects, and layout limits, so verify critical designs with measurements.